PriEsT: an interactive decision support tool to estimate priorities from pairwise comparison judgments

Pairwise comparison (PC) is a well-established method to assist decision makers (DMs) in estimating their preferences. This paper considers the rationale, design, and evaluation of an open-source priority estimation tool, PriEsT, which has been developed to offer new features related to the PC method. PriEsT is able to assist DMs in interactively identifying and revising their judgments based on different consistency measures and graphical aids. When inconsistency cannot be improved due to practical limitations, PriEsT offers a wide range of Pareto-optimal solutions based on multiobjective optimization, unlike other tools that offer only a single solution. DMs have the flexibility to select any of these nondominated solutions according to their requirements. The features of PriEsT have been demonstrated and evaluated through its application to a real-world case study: the selection of the most appropriate telecom infrastructure for rural areas. This case study using PriEsT has highlighted the presence of intransitive judgments in the acquired data, and the correction of these judgments has led to a different ranking of the available alternatives

Group aggregation of pairwise comparisons using multi-objective optimization

AbstractIn group decision making, multiple decision makers (DMs) aim to reach a consensus ranking of alternatives in a decision problem. The differing expertise, experience and, potentially conflicting, interests of the DMs will result in the need for some form of conciliation to achieve consensus. Pairwise comparisons are commonly used to elicit values of preference of a DM. The aggregation of the preferences of multiple DMs must additionally consider potential conflict between DMs and how these conflicts may result in a need for compromise to reach group consensus.We present an approach to aggregating the preferences of multiple DMs, utilizing multi-objective optimization, to derive and highlight underlying conflict between the DMs when seeking to achieve consensus. Extracting knowledge of conflict facilitates both traceability and transparency of the trade-offs involved when reaching a group consensus.Further, the approach incorporates inconsistency reduction during the aggregation process to seek to diminish adverse effects upon decision outcomes. The approach can determine a single final solution based on either global compromise information or through utilizing weights of importance of the DMs.Within multi-criteria decision making, we present a case study within the Analytical Hierarchy Process from which we derive a richer final ranking of the decision alternatives

A framework for defining weights of decision makers in group decision-making, using consistency between different multicriteria weighting methods

Most forest operations are complex problems that require the weights of relevant criteria - representing trade-offs between various economic, ecological, and social aspects of the problem - to be defined. Usually this is done by using multicriteria weighting method(s) in a group (participatory) context in order to include different opinions and to minimize risk of poor individual judgments. Furthermore, in group decision-making, the weights of decision makers (DMs) must be defined. However, no consensus exists on the best way to determine related weights assigned to DMs. For that purpose, we propose the consistency-based group decision-making framework (CGDF), which uses the expertise of a DM to weight the responses of the DM when deriving an overall group decision. The novel part of CGDF is the inter-weights consistency method (ICM) for evaluating the expertise of a DM based on the consistency of the weights the DM assigns to different criteria using different multicriteria weighting methods. We demonstrate the utility of ICM and CGDF by applying them to a decision-making problem from Swedish forest operations - defining weights of criteria relevant for designing the machine-trail network for driving in the forest terrain

Preference elicitation from pairwise comparisons in multi-criteria decision making

Decision making is an essential activity for humans and often becomes complex in the presence of uncertainty or insufficient knowledge. This research aims at estimating preferences using pairwise comparisons. A decision maker uses pairwise comparison when he/she is unable to directly assign criteria weights or scores to the available options. The judgments provided in pairwise comparisons may not always be consistent for several reasons. Experimentation has been used to obtain statistical evidence related to the widely-used consistency measures. The results highlight the need to propose new consistency measures. Two new consistency measures - termed congruence and dissonance - are proposed to aid the decision maker in the process of elicitation. Inconsistencies in pairwise comparisons are of two types i.e. cardinal and ordinal. It is shown that both cardinal and ordinal consistency can be improved with the help of these two measures. A heuristic method is then devised to detect and remove intransitive judgments. The results suggest that the devised method is feasible for improving ordinal consistency and is computationally more efficient than the optimization-based methods. There exist situations when revision of judgments is not allowed and prioritization is required without attempting to remove inconsistency. A new prioritization method has been proposed using the graph-theoretic approach. Although the performance of the proposed prioritization method was found to be comparable to other approaches, it has practical limitation in terms of computation time. As a consequence, the problem of prioritization is explored as an optimization problem. A new method based on multi-objective optimization is formulated that offers multiple non-dominated solutions and outperforms all other relevant methods for inconsistent set of judgments. A priority estimation tool (PriEsT) has been developed that implements the proposed consistency measures and prioritization methods. In order to show the benefits of PriEsT, a case study involving Telecom infrastructure selection is presented.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

A Pairwise Comparison Matrix Framework for Large-Scale Decision Making

abstract: A Pairwise Comparison Matrix (PCM) is used to compute for relative priorities of criteria or alternatives and are integral components of widely applied decision making tools: the Analytic Hierarchy Process (AHP) and its generalized form, the Analytic Network Process (ANP). However, a PCM suffers from several issues limiting its application to large-scale decision problems, specifically: (1) to the curse of dimensionality, that is, a large number of pairwise comparisons need to be elicited from a decision maker (DM), (2) inconsistent and (3) imprecise preferences maybe obtained due to the limited cognitive power of DMs. This dissertation proposes a PCM Framework for Large-Scale Decisions to address these limitations in three phases as follows. The first phase proposes a binary integer program (BIP) to intelligently decompose a PCM into several mutually exclusive subsets using interdependence scores. As a result, the number of pairwise comparisons is reduced and the consistency of the PCM is improved. Since the subsets are disjoint, the most independent pivot element is identified to connect all subsets. This is done to derive the global weights of the elements from the original PCM. The proposed BIP is applied to both AHP and ANP methodologies. However, it is noted that the optimal number of subsets is provided subjectively by the DM and hence is subject to biases and judgement errors. The second phase proposes a trade-off PCM decomposition methodology to decompose a PCM into a number of optimally identified subsets. A BIP is proposed to balance the: (1) time savings by reducing pairwise comparisons, the level of PCM inconsistency, and (2) the accuracy of the weights. The proposed methodology is applied to the AHP to demonstrate its advantages and is compared to established methodologies. In the third phase, a beta distribution is proposed to generalize a wide variety of imprecise pairwise comparison distributions via a method of moments methodology. A Non-Linear Programming model is then developed that calculates PCM element weights which maximizes the preferences of the DM as well as minimizes the inconsistency simultaneously. Comparison experiments are conducted using datasets collected from literature to validate the proposed methodology.Dissertation/ThesisPh.D. Industrial Engineering 201